A 1-parameter approach to links in a solid torus
Geometric Topology
2008-10-23 v3
Abstract
To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a study of codimension~2 singularities of link diagrams. For closed braids with a fixed number of strands, trace graphs can be recognized up to equivalence excluding one type of moves in polynomial time with respect to the braid length.
Keywords
Cite
@article{arxiv.math/0606381,
title = {A 1-parameter approach to links in a solid torus},
author = {T. Fiedler and V. Kurlin},
journal= {arXiv preprint arXiv:math/0606381},
year = {2008}
}
Comments
38 pages, 14 figures, the applications on closed braids were moved to another paper `Recognising trace graphs of closed braids' (arXiv:0808.2713), more details were added on versal deformations of codimension 2 singularities